# Boolean algebra -Sum of products form - theorem

1. Oct 22, 2010

### icelated

1. The problem statement, all variables and given/known data

Show the following is true using theorems. State which theorem you use at each step.

A'BD' + BCD + ABC' + AB'D = A'BD' + BCD + ABC' + AB'D + BC'D' + A'BC + ABD

2. Relevant equations

3. The attempt at a solution

I am very new to boolean algebra and very confused. This is a digital logic course for software engineering students. I dont know where to begin. Working on the left side first would i need to expand it to make sure that every sum of product has the same amount of variables? Or, should i just try to combine like variables and work it out? Should i work with all the terms before the = like: ( A'BD' + BCD + ABC' + AB'D) and pull out a like term like A?

I just dont understand how to do this. Looking at the different theorems in the book dont help any. Can you give me some steps on how to solve this? Maybe, help me work out the first sum of products?(before the = ) than i can see how its done so i can finish the rest of it. I learn by example.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 7, 2011

### KDye

Ok, the best way to go about solving this problem is to put together a list of all the things that you can do with Boolean Algebra. When you have a properties list, it'll be a lot easier to manipulate and simplify. Here's a site that'll help you make your list. http://www.ee.surrey.ac.uk/Projects/Labview/boolalgebra/
The way I solved this was to use the distributive property on the right hand side first. It'll help with the cancellations. You want to make the right side look like the left side. Try this first.